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Ulleksa [173]
3 years ago
5

An old house in Pomona, CA is inhabited by a variety of ghosts. Ghost appearances occur in the house according to a Poisson proc

ess having a rate of 1.4 ghosts per hour. A professor from Cal Poly Pomona has developed a device that can be used to detect ghost appearances. Suppose it is now 1:00 p.m. and the last ghost appearance (the 6th overall) was at 12:35 p.m.
What is the probability that the 7th ghost will appear before 1:30 p.m., to the nearest three decimal places?
Mathematics
1 answer:
shutvik [7]3 years ago
8 0

Answer:

The probability is 0.503

Step-by-step explanation:

If the ghost appearances occur in the house according to a Poisson process with mean m, the time between appearances follows a exponential distribution with mean 1/m. so, the probability that the next ghost appearance happens before x hours is equal to:

P(X\leq x)=1-e^{-xm}

Then, replacing m by 1.4 ghosts per hour we get:

P(X\leq x)=1-e^{-1.4x}

Additionally, The exponential distribution have a memoryless property, so if it is now 1:00 p.m. and we want the probability that ghost appear before 1:30 p.m., we need to find the difference in hours from 1:00 p.m and 1:30 p.m. no matter that the last ghost appearance was at 12:35 p.m.

Therefore, there are 0.5 hours between 1:00 p.m. and 1:30 p.m, so the probability that the 7th ghost will appear before 1:30 p.m is calculated as:

P(x\leq 0.5)=1-e^{-1.4*0.5} =0.503

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Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children. Let BBG ind
Gemiola [76]

Answer:

(a)

S = \{GGG, GGB, GBG, GBB, BBG, BGB, BGG, BBB\}

(b)

i.

1\ girl = \{GBB, BBG, BGB\}

P(1\ girl) = 0.375

ii.

Atleast\ 2 \ girls = \{GGG, GGB, GBG, BGG\}

P(Atleast\ 2 \ girls) = 0.5

iii.

No\ girl = \{BBB\}

P(No\ girl) = 0.125

Step-by-step explanation:

Given

Children = 3

B = Boys

G = Girls

Solving (a): List all possible elements using set-roster notation.

The possible elements are:

S = \{GGG, GGB, GBG, GBB, BBG, BGB, BGG, BBB\}

And the number of elements are:

n(S) = 8

Solving (bi) Exactly 1 girl

From the list of possible elements, we have:

1\ girl = \{GBB, BBG, BGB\}

And the number of the list is;

n(1\ girl) = 3

The probability is calculated as;

P(1\ girl) = \frac{n(1\ girl)}{n(S)}

P(1\ girl) = \frac{3}{8}

P(1\ girl) = 0.375

Solving (bi) At least 2 are girls

From the list of possible elements, we have:

Atleast\ 2 \ girls = \{GGG, GGB, GBG, BGG\}

And the number of the list is;

n(Atleast\ 2 \ girls) = 4

The probability is calculated as;

P(Atleast\ 2 \ girls) = \frac{n(Atleast\ 2 \ girls)}{n(S)}

P(Atleast\ 2 \ girls) = \frac{4}{8}

P(Atleast\ 2 \ girls) = 0.5

Solving (biii) No girl

From the list of possible elements, we have:

No\ girl = \{BBB\}

And the number of the list is;

n(No\ girl) = 1

The probability is calculated as;

P(No\ girl) = \frac{n(No\ girl)}{n(S)}

P(No\ girl) = \frac{1}{8}

P(No\ girl) = 0.125

7 0
3 years ago
Bob had 18 crackers Sam eat 1/6 of the crackers and sue ate 1/3 of the crackers. how many crackers did Bob have left
Lapatulllka [165]
We can add 1/6 & 1/3 together to find out the total amount of crackers that were eaten:

1/6 + 1/3   (Find the Common Denominator. In this case it is 6.) 
= 1/6 + 2/6
= 3/6 (Now find the Lowest Terms. Both 6 & 3 divide into 3)
= 1/2 (In Lowest Terms)

This means that 1/2 of the Crackers have been eaten.

1/2 of 18 = 9 

Therefore, Bob has 9 Crackers left. 
6 0
3 years ago
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Thepotemich [5.8K]

hope it helps you!!!!!!!!!!

4 0
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8 0
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